Gerd Rudolph

Partial-wave analysis of the 3π system produced in the reaction π+p → (π+π+π−)p at 8, 16 and 23 GeV/c

Abstract A partial-wave analysis has been made of the (3π) system produced in the reaction π + p → ( π + π + π − )p at 8, 16 and 23 GeV/ c using the Illinois partial-wave analysis program. The (3π) systems is in about 93% of the cases in the unnatural spin-parity states 0 − , 1 + , 2 − and 3 + and is produced in about 100% of the cases by natural parity exchange. For all J P states, the differential cross section d σ /d t ′ peaks at small tt ′, except for 2 + D which has a dip at t ′ ≈ 0. The cross sections for J P = 1 + , 2 + and 2 − in the A 1 , A 2 and A 3 regions, respectively, all have similar energy dependence, p lab − n , with n = 0.3 ± 0.2. The weak variation of the 1 + S phase across the 1.0–1.2 GeV mass region, suggests that A 1 cannot be considered as a single resonance, while the phase variation of 2 + D (ϱπ) in the A 2 mass region is consistent with resonance behaviour. In the A 3 region, the behaviour of the 2 − S and 2 − P phases is complex and further work is needed to understand the mechanisms involved there.

A Gauge Model for Quantum Mechanics on a Stratified Space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified Kähler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure yields a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is SU(2), we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.

On a connection governing parallel transport along 2 × 2 density matrices

Abstract We investigate a connection governing parallel transport along mixed states recently defined by Uhlmann for the case of 2 × 2 matrices. We discuss the underlying bundle structure including singular orbits, show an interesting relation to instantons and prove that the connection fulfils the source-free Yang-Mills equation with respect to the Riemannian metric on the space of density matrices induced by the Bures metric.

Charge superselection sectors for QCD on the lattice

We study quantum chromodynamics (QCD) on a finite lattice Λ in the Hamiltonian approach. First, we present the field algebra AΛ as comprising a gluonic part, with basic building block being the crossed product C*-algebra C(G)⊗αG, and a fermionic (CAR-algebra) part generated by the quark fields. By classical arguments, AΛ has a unique (up to unitary equivalence) irreducible representation. Next, the algebra OΛi of internal observables is defined as the algebra of gauge invariant fields, satisfying the Gauss law. In order to take into account correlations of field degrees of freedom inside Λ with the “rest of the world,” we must extend OΛi by tensorizing with the algebra of external gauge invariant operators. This way we construct the full observable algebra OΛ. It is proved that its irreducible representations are labelled by Z3-valued boundary flux distributions. Then, it is shown that there exist unitary operators (charge carrying fields), which intertwine between irreducible sectors leading to a classif...

A class of connections governing parallel transport along density matrices

A class of connections governing parallel transport along nondegenerate density matrices is discussed. These connections are given by certain analytic functions. We develop a calculus for operator‐valued differential forms, which enables us to calculate the curvature of these connections. The class under consideration contains a non‐Abelian generalization of Berry’s phase recently proposed by Uhlmann.

On the stratified classical configuration space of lattice QCD

Abstract The stratified structure of the configuration space G N = G × ⋯ × G reduced with respect to the action of G by inner automorphisms is investigated for G = SU ( 3 ) . This is a finite dimensional model coming from lattice QCD. First, the stratification is characterized algebraically, for arbitrary N . Next, the full algebra of invariants is discussed for the cases N = 1 and N = 2 . Finally, for N = 1 and N = 2 , the stratified structure is investigated in some detail, both in terms of invariants and relations and in more geometric terms. Moreover, the strata are characterized explicitly using local cross sections.

On the Gauss law and global charge for quantum chromodynamics

The local Gauss law of quantum chromodynamics on a finite lattice is investigated. It is shown that it implies a gauge invariant, additive law giving rise to a gauge invariant

On the structure of the observable algebra of QCD on the lattice

{\mathbb Z}_3

K∗(890) production in K−p → NKπ at 16 GeV/c

-valued global charge in QCD. The total charge contained in a region of the lattice is equal to the flux through its boundary of a certain

Charge Superselection Sectors for Scalar QED on the Lattice

{\mathbb Z}_3